How to evaluate:

∫∫∫ xyz/(x^2+y^2)^1/2 dv

E

where E is the solid "quarter-cylinder" in the first octant bounded by a cylinder of radius a>o with axis long the z axis, the planes y=0,x=0,z=0 and z=b, wiht b>0.

Thankyou very much!

Printable View

- Nov 20th 2008, 10:59 AMiwondercylindrical or spherical coordinates problem
How to evaluate:

∫∫∫ xyz/(x^2+y^2)^1/2 dv

E

where E is the solid "quarter-cylinder" in the first octant bounded by a cylinder of radius a>o with axis long the z axis, the planes y=0,x=0,z=0 and z=b, wiht b>0.

Thankyou very much! - Nov 20th 2008, 12:23 PMJD-Styles
The best way to tackle this one is to change to cylindrical coordinates. So we'd get:

- Nov 20th 2008, 10:58 PMiwonder
thankyou!

i got it so far, but how do u get p^2 for the third limit of integration? is that only be p??? - Nov 23rd 2008, 10:22 AMJD-Styles
There's one p from x, on from y, one from the change to spherical coordinates (that comes with d phi), so that's p^3 in the numerator. Then in the denominator you have one p from (x^2+y^2)^1/2. So in total you have p^(3-1)=p^2